In modern electronically controlled automobiles, a sensor is provided in an exhaust pipe to detect the air-fuel ratio or the oxygen concentration of the exhaust gas emitted from an internal combustion engine, and the amount of the fuel fed to the internal combustion engine is controlled by feedback relying upon the sensor output, so that the air-fuel ratio of the exhaust gas is maintained near a target air-fuel ratio in order to improve the engine performance such as emission of the exhaust gas and the fuel efficiency. The modern air-fuel ratio feedback control systems are designed by modeling the response characteristics according to which the air-fuel ratio of the exhaust gas varies following a change in the amount of feeding the fuel which is the object to be controlled, after the dead time+1st-order delay characteristics (or 2nd-order delay characteristics). Therefore, if the response characteristics of the sensor vary due to deteriorated characteristics of the sensor that detects the air-fuel ratio of the exhaust gas or due to the faulty sensor, the precision for detecting the air-fuel ratio is deteriorated and, hence, the precision for controlling the air-fuel ratio is deteriorated, causing a deterioration in the engine performance.
JP-8-177575A discloses a method according to which a change in the sensor output (rate of change) is detected after having detected a change in the amount of fuel fed into the internal combustion engine (beginning of fuel cut or end of fuel cut) to determine the deterioration in the response characteristics of the sensor.
According to the method of detecting sensor response characteristics disclosed in JP-8-177575A, however, a change in the sensor output is simply detected after a change in the amount of fuel supply without detecting the response characteristics (dead time and the 1st-order delay characteristics or the 2nd-order delay characteristics) on which the design of the air-fuel ratio feedback control system is based. It is therefore difficult to precisely detect the deterioration in the air-fuel ratio feedback controllability caused by the deteriorated response characteristics of the sensor or by the faulty sensor. Further, the above method is not detecting the response characteristics (dead time and the 1st-order delay characteristics or the 2nd-order delay characteristics) on which the design of the air-fuel ratio feedback control system is based. It is therefore difficult to detect the response characteristics or to correct the air-fuel ratio feedback control parameter relying upon the response characteristics that are detected.